The way I play Lulu during the early levels is agressive. I try harassing the opponent's life down with normal hits and I avoid wasting my mana. In case the AD Carry pushes the lane, I ward early, especially is the enemy jungler starts with the buff closest to our lane.
Ι place one ward at dragon/tribush (depending on side) so we have vision and the time to get back to our turret in case of a gank.
Ιf the lane stays even and no side is pushing, there is a chance for a lane gank to happen. So it would be wise to keep a ward and the opponent's side brush.
A good time to go back is when you are out of wards.
Something very important about the support role is keeping timers for buffs, dragons and Baron Νashor. Blue and Red buff respawn in 5 minutes. Drake is on 6 and Baron needs 7.
You ward depending on the game. If you are ahead wards should be more offensive. This means warding the opposing jungle. Some good spots for agressive warding is their buffs and wraith brush, so your team can counter jungle, and the jungle entrances.
On the other hand, defensive wards would be on your jungle entrances and buffs.
There should always be wards on Dragon and Baron.
Oracle's is a great investment as you can get rid of wards and rob the opponents from their vision.
In teamfights, your main objective is mostly protecting your AD Carry. Lulu can easiliy do that as she has a shield, a movement speed increase and her ulti, which gives AoE slow around your teammate and lots of health.
Using your ultimate is a matter of judgement. Depends on where you think it is needed most. I mostly cast it on AD carries or the initator. Usually the initator goes in first and takes most of the focus. So my ultimate makes him last longer if he takes too much damage at start. If that's not the case, I choose the AD because if he lives we usually win the fight.
Tips & Tricks
The ability combos you can use on Lulu is mostly Help, Pix! with Glitterlance. Placing Pix with Help, Pix! on an ally, opponent or any minion, you can use Glitterlance from the spot Pix is, greatly extending the range.
Also, during the laning phase, Whimsy transforms opponents into squirrels for a few seconds, enough time to save your AD carry from lots of damage he could have taken, for example, when he is CC'ed and/or initiated on by an enemy support like Alistar, Leona and Taric, Whimsy stops the opposing AD from damaging yours, giving him enough time to get away from the CC.
Also, dont forget, extra hp on Wild Growth isn't a healing effect so it isnt stopped by ignite.
Finally, Help, Pix! reveals heroes that like going invisible, like Akali.
A counter against Lulu is Taric as he can easily stun her out of position and get her low enough to not be able to be used to her fullest potential (Harassing).
Soraka is also very strong against Lulu because of her lane staying power, due to her healing and mana replenishment. After some levels and with proper management you can win the lane, abusing the time her skills are on cooldown.
Finally Janna is a counter to Lulu, not in lane, but later, on fights where she 'll be able to reduce Lulu's effectiveness as her skills demand of her teammates to be close to the opponents for full effect.
She's very good against Skarner as her ultimate prevents the target of Skarner's ultimate to be immediately killed.
She partners very well with Graves. Grave's passive works nice with Lulu's shield and also he is a close range AD.
Αlso she matches nicely with heroes like Shyvana and Jax as they have a way to get in the midst of the enemy team, making them prime targets for Lulu's ultimate.